Macromolecular characterization of liquid chromatography consists of analyzing the fractionated sample that elutes from a chromatography column with serially connected detectors that each measure different properties of the sample. A typical detector chain that can be used to measure the molar mass and radius of gyration consists of a multi-angle light scattering detector (MALS) and a refractive index detector. There are many other detectors that can also be added to the analysis chain, including but not limited to, UV absorption, differential viscometry, quasi-elastic light scattering, and mass spectrometry. However in the process of flowing between detectors the sample, fractionated by the columns, becomes increasingly remixed as the sample is sheared in the tubing and mixed by passage through the various measurement cells. This is the problem of inter-detector band broadening which is distinct from the related problem of mixing and broadening within the chromatography columns, which is typically referred to as column broadening.
In order to extract physical parameters one must often compare the signal from different detectors for the same physical aliquot of sample as it passes through the analysis chain. However since the sample is being slowly remixed there are two effects that will affect this comparison. The first is that a peak of uniform composition, but varying concentration, will be affected by having the peak shape broaden. In general the first detector will measure the narrowest peak, which will be subsequently increased as the sample progresses through the detector chain. For example, in light scattering analysis, the molecular weight of the sample at low concentration is proportional to the ratio of the light scattering signalM(t)∝LS(t)/RI/(t).  (1)where M(t) is the molar mass of the sample as a function of time, LS(t) is the light scattering signal as a function of time, and RI/(t) is the differential refractive index detector as a function of time. Consider what happens if a monodisperse sample is measured by an analysis chain that consists of light scattering instrument followed by a refractive index detector. Since the sample is monodisperse, the molar mass across the peak is constant so that in this case M(t)=M and we find that the two detector responses should be directly proportional to each other LS(t)∝RI(t). This means if we measure a peak and scale them to the sample amplitude, they should overlay perfectly. However, in the case that there is inter-detector band broadening, the peak shape of the downstream detector, being broadened, is no longer directly proportional to the upstream detector and we find that the RI peak is broader than the LS peak. When the molecular weight analysis is performed, this leads to an error in the derived molar mass. In the literature, there have been various methods proposed for addressing this problem that consists of modeling the mixing that occurs, for example, see U.S. Pat. No. 7,386,427 by Trainoff, “Method for correcting the effects of interdetector band broadening,” and applying mathematical corrections the compensate for the change in peak shape. These methods work well as long as the broadening is small compared to the peak width. A rough rule of thumb is that if the broadening increases the peak width by 20% or less, the numerical corrections can correct for the effect.
The second effect of broadening, is to mix two adjacent peaks of different composition. This is equivalent to a loss of resolution. This is a more difficult problem because numerical modeling typically assumes that the sample that passes through each detector is well fractionated and that at any given time the sample in each detector is nearly monodisperse. When the inter-detector broadening makes the sample polydisperse, it is much more difficult to correct numerically.
A trend in liquid chromatography is towards narrower bore columns that shorten run times and increase resolution. A typical standard bore chromatography column has an internal diameter of 4-5 mm and requires a solvent flow rate of around 1 ml/min for optimal resolution. When a sample is injected into such a system the individual components are fractionated into a series of peaks that each have an eluted volume of around 1 ml. In order to avoid excessive inter-detector broadening the analysis instruments are designed to have as low an internal volume as is possible. However even if the internal volume of the cell is small, the effective mixing volume may be larger than the physical volume depending on the flow characteristics of the cell. For example the Optilab® T-rEX™ differential refractive index cell manufactured by Wyatt Technology has an internal volume of 7.5 μl, but the triangular shape of the cell makes it difficult to flush the corners which results in an effective mixing volume of around 15 μl for a flow rate of 1.0 ml/min when there is turbulent mixing in the cell, and as much as 200 μl for a flow rate of 0.1 ml/min, which results in laminar flow in the cell that does not adequately flush the corners. In general, the effective mixing volume is closer to the physical volume for higher flow rates.
The total inter-detector broadening is a combination of the mixing that occurs as the sample exits the first cell, travels through the capillary tubing to the second instrument and then is mixed entering the second cell. For the example of a Wyatt Technology DAWN® HELEOS® multi-angle light scattering (MALS) instrument followed by an Optilab T-rEX DRI system, the effective inter-detector broadening for a flow rate of 1.0 ml/min is roughly 50 μl, which is only 5% of the typical peak width of 1.0 μl. This is well less than the 20% rule of thumb mentioned earlier and the numerical band broadening correction works well. However for a narrow bore chromatography column such as the Waters Acquity column that has an internal diameter of 3.0 mm and a flow rate of 0.3 ml/min, the peak widths drop by roughly a factor of 10 to approximately 100 μl. In this case, the inter-detector broadening actually increases somewhat due to the lower flow rate, but even at 50 μl mixing volume it represents 50% of the peak width and the numerical broadening corrections perform poorly. The peaks are highly distorted and the there is substantial loss of resolution. Clearly there is a strong incentive to make the effective broadening volume as small as possible, but at some point instrumental design and manufacturing considerations limit how small an experimental cell can be. It is the subject of this invention to present a method of controlling the effects of inter-detector band broadening.